• Identify the line that just touches a curve at one point by looking at how nearby lines approach it
• Describe how integration can be used to calculate the area under a curve

Caitlin Clark, regarded as one of the greatest collegiate players of all time, joined the Indiana Fever of the Women’s National Basketball Association in 2024. When she shoots a basketball, the height of the ball (in feet) $t$ seconds after it leaves her hands is given by 

$h(t)=-16t2+24t+8$

The ball arcs through the air and passes cleanly through the basket which is $10$ feet above the ground. It’s a swish!

Caitlin Clark is dealing with fractions of a second here! For the following exercises, complete any calculations with values rounded to five decimal places. Give your final answers rounded to the nearest hundredth.